Global (and local) analyticity for second order operators constructed from rigid vector fields on products of tori

We prove global analytic hypoellipticity on a product of tori for partial differential operators which are constructed as rigid (variable coefficient) quadratic polynomials in real vector fields satisfying the Hörmander condition and where satisfies a ``maximal' estimate. We also prove an analyticity result that is local in some variables and global in others for operators whose prototype is

(with analytic , naturally, but not identically zero). The results, because of the flexibility of the methods, generalize recent work of Cordaro and Himonas in [4] and Himonas in [8] which showed that certain operators known not to be locally analytic hypoelliptic (those of Baouendi and Goulaouic [1], Hanges and Himonas [6], and Christ [3]) were globally analytic hypoelliptic on products of tori.

     

Chemistry of 1-Alkoxy-1-glycosyl Radicals: The Manno- and Rhamnopyranosyl Series. Inversion of alpha- to beta-Pyranosides and the Fragmentation of Anomeric Radicals

The formation and stereoselective quenching of 1-mannopyranosyl radicals by a tributyltin hydride-mediated intramolecular 1,5-hydrogen abstraction sequence is described. A competing process is 1,4-hydrogen atom abstraction leading principally to glucopyran-2-ulosides. Fragmentation of the anomeric radical resulting in the formation of ring opened products is a problem in certain series. The chemistry is dictated to a considerable extent by the nature of the protecting groups employed with the 4,6-benzylidene series and, for rhamnose, the Ley 3,4-dispiroketal, being particularly susceptible to the 1,4-hydrogen atom abstraction but less to the fragmentation. Photochemical conditions are described, in which these side reactions are practically eliminated, and applied to the inversion of an alpha- to a beta-mannoside in a disaccharide.     

LP modeling languages for personal computers: A comparison

The purpose of this paper is to compare and contrast the modeling capabilities of seven algebraic modeling languages (ML) available today, namely, AMPL, GAMS, LINGO, LPL, MPL, PC-PROG and XPRESS-LP. In general, these MLs do an excellent job of providing an interface with which the modeler can specify an algebraically formatted linear program (LP). That is, each ML provides a substantial improvement in time and convenience over the matrix generator/report writers of the last few decades. Further, each of the MLs provides: (1) significant flexibility in model specification, instantiation and modification, (2) effective and efficient conversion from algebraic to solver format, and (3) an understandable and, for the most part, self-documenting model representation. In addition, each of the MLs is constantly being updated and upgraded to provide additional capabilities sought by practitioners and users. However, as shown in the fifteen tables provided in the body of this paper, each ML has its own set of competitive advantages. For example, the most integrated environments (i.e. those integrating the modeling language with a full-screen editor, data import capabilities and a solver) are provided by LINGO and PC-PROG. The most user-friendly interfaces are provided by MPL and PC-PROG, both of which provide window-based interfaces to create models and pop-up windows to display error messages; MPL also uses pull-down menus to specify various operations, whereas PC-PROG uses function keys for operational control. Package costs are led by a current (March, 1991) introductory offer from LINGO. Modeling effectiveness, especially with respect to flexibility in specifying arithmetic statements, is led by GAMS and LPL. Model compactness, as measured by the number of lines required to specify a model, is led by AMPL, LPL, MPL and PC-PROG; LPL, MPL and PC-PROG also provide context sensitive editors which automatically position the cursor where the error was detected. And finally, the most comprehensive user documentation is provided by GAMS, whereas GAMS, LINGO and LPL provide extensive libraries of sample models for those users who learn by example.     

Lattice size estimates for Gabor decompositions

It is shown that the Gabor frame operator for frames with lattice such thatab=1/N for some integerN1 is continuous on the modulation spaces ([9], [20]) whenever the basic functiong is a Schwartz function and (g, a, b) generates a frame forL ² (R). From this a sufficient condition on the lattice is given which guarantees that one has a Banach frame for the modulation spaces of Feichtinger.This work was supported by NSF grant # DMS-8916968 while the author was visiting Yale University.     

The reaction of allenylsilanes with α,β-unsaturated acylsilanes: new annulation approaches to five and six-membered carbocyclic compounds

The reaction of α,β-unsaturated acylsilanes with allenylsilanes can be directed to produce either five or six-membered carbocyclic compounds.     

Crystal structure of (1rs, 14sr, 17rs, 18rs)-2,20-dioxa-17-methyltricyclo [16,3,0,0] heneicosa-15-ene-3,19,21-trione; a macrocyclic lac

An X-ray study of the major product of the intramolecular Diels-Alder reaction of the diene-anhydride (2) has confirmed it as being the desired cytochalasan analogue (3). In particular the cyclisation has been regioselective, and has taken place via the endo transition state to generate the adduct with the correct relative configurations at the four chiral centres. Details of the conformational geometry of (3) are discussed.     

Assembly of colloidal particles into microwires using an alternating electric field

We have investigated the dielectrophoretic assembly of colloidal gold, carbon black, and carbon nanotubes into electrical wires. The resulting microwires have diameters less than 1 microm, with lengths ranging from 5 microm to 3 mm. Current-voltage curves for these wires indicate an ohmic response, where the resistance is determined by the type of colloid and by the frequency of the alternating field used to grow the wires. The predicted frequency dependence of dielectrophoresis is confirmed by experiment. Measurements of the threshold voltage for initial wire growth are also presented. These experiments demonstrate that a variety of nanoparticles can be assembled into microwires for sensor applications.     

Reactions of Charged Substrates. 4. The Gas-Phase Dissociation of (4-Substituted benzyl)dimethylsulfoniums and -pyridiniums

The relative rates for the gas-phase dissociation RX(+) --> R(+) + X degrees of five (4-Y-substituted benzyl)dimethysulfoniums (Y = MeO, Me, H, Cl, and NO(2)) and 24 (4-Y-substituted benzyl)-3'-Z-pyridiniums (complete series for Z = CN, Cl, CONH(2), and H, and 4-methoxy- and 4-nitrobenzyls for Z = F and CH(3)CO) were measured using liquid secondary ion mass spectrometry. The Hammett plot (vs deltaDeltaG degrees or sigma(+)) is linear for the sulfoniums, but plots for the four pyridinium series have a drastic break between the 4-Cl and 4-NO(2) substrates. Br?nsted-like plots for the pyridiniums show a strong leaving group effect only for 4-nitrobenzyls. An analysis of these linear free energy relations with supporting evidence from semiempirical computations suggests that collisionally activated pyridinium substrates dissociate by two pathways, direct dissociation and through an ion-neutral complex intermediate. Comparison of these results with results for the solution reactions of some of these compounds shows that the mechanism is different in the gas and solution phases. Sufficient experimental data are not available to assign a mechanism for dissociation to the sulfonium series, but computational results show characteristics of a direct dissociative mechanism.